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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
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Category theory and set theory: just a different language, or different foundation of mathem...
As you are asking for references, the following book might be of interest to you:
Basic Category Theory from Tom Leinster (I think from 2014 or 2017).
I like the way he introduces category theory, and …